Calculation of  ,
,  and
 and  from a diameter
 from a diameter  and the reference velocity
 and the reference velocity  for a circular duct flow with smooth wall (use for inlet boundary conditions).  
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 for a circular duct flow with smooth wall (use for inlet boundary conditions).  
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 Collaboration diagram for turbulence_bc_ke_hyd_diam:
 Collaboration diagram for turbulence_bc_ke_hyd_diam:| Public Member Functions | |
| subroutine | turbulence_bc_ke_hyd_diam (uref2, dh, rho, mu, ustar2, k, eps) | 
Calculation of  ,
,  and
 and  from a diameter
 from a diameter  and the reference velocity
 and the reference velocity  for a circular duct flow with smooth wall (use for inlet boundary conditions).
 for a circular duct flow with smooth wall (use for inlet boundary conditions). 
Both  and
 and  are returned, so that the user may compute other values of
 are returned, so that the user may compute other values of  and
 and  with
 with  .
.
We use the laws from Idel'Cik, i.e. the head loss coefficient  is defined by:
 is defined by: 
![\[ |\dfrac{\Delta P}{\Delta x}| = \dfrac{\lambda}{D_H} \frac{1}{2} \rho U_{ref}^2 \]](form_121.png) 
then the relation reads  .
.  depends on the hydraulic Reynolds number
 depends on the hydraulic Reynolds number  and is given by:
 and is given by:
 
 
![\[ \lambda = \dfrac{64}{Re} \]](form_126.png) 
 
 
![\[ \lambda = \dfrac{1}{( 1.8 \log_{10}(Re)-1.64 )^2} \]](form_128.png) 
 , we complete by a straight line
, we complete by a straight line 
![\[ \lambda = 0.021377 + 5.3115. 10^{-6} Re \]](form_130.png) 
From  , we can estimate
, we can estimate  and
 and  from the well known formulae of developped turbulence
 from the well known formulae of developped turbulence
![\[ k = \dfrac{u^{\star 2}}{\sqrt{C_\mu}} \]](form_132.png) 
![\[ \varepsilon = \dfrac{ u^{\star 3}}{(\kappa D_H /10)} \]](form_133.png) 
| [in] | uref2 | square of the reference flow velocity | 
| [in] | dh | hydraulic diameter   | 
| [in] | rho | mass density   | 
| [in] | mu | dynamic viscosity   | 
| [out] | ustar2 | square of friction speed | 
| [out] | k | calculated turbulent intensity   | 
| [out] | eps | calculated turbulent dissipation   | 
| subroutine turbulence_bc_ke_hyd_diam | ( | real(c_double), value | uref2, | 
| real(c_double), value | dh, | ||
| real(c_double), value | rho, | ||
| real(c_double), value | mu, | ||
| real(c_double) | ustar2, | ||
| real(c_double) | k, | ||
| real(c_double) | eps | ||
| ) |